An Au and Aharonov type perturbation theory for the two-dimensional scalar wave equation is described. As an application, it is shown that the 'effective refractive index' method is related to the first-order correction to the eigenstate. In addition, the authors compare results obtained for the gain G in a typical laser structure using either the present theory or averaging the imaginary part of the refractive index over the fields ('average modal gain' G OVER BAR ). The results agree to about 8% in a test case where the perturbative result is, in fact, exact. It is concluded that the perturbative approach will, in general, be more reliable.